2023 KSS P1 Q10

2023 KSS P1 Q10

Secondary 4
6 marks

In the triangle \(ABC\), angle \(B=90^\circ\), \(AB=(\sqrt7+2)\) cm and \(BC=(\sqrt7-2)\) cm.

  1. Find the exact length of \(AC\).[3]
  2. Express \(\tan A\) in the form \(\dfrac{a+b\sqrt7}3\), where \(a\) and \(b\) are integers.[3]

Solution:

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Answer:(i) \(\sqrt{22}\text{ cm}\). (ii) \(\dfrac{11-4\sqrt7}3\).

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